Finite Group Databasebeta

← #14664925

Subgroups — #14664925

Order 2816.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073978C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066645C212yesmaximal
4#13066642C212yesmaximal
5C11×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic
8C11×#423—21no—
9C2×C11×#101—21no—
10#10622843—21no—
11#10622599C411yescharacteristic
12#10622599C2211yescharacteristic
13#10622592C411yescharacteristic
14#10622592C2211yescharacteristic
15#10622586—21no—
16#10622549C411yescharacteristic
17#10622546—21no—
18#10622546—21no—
19#10622538—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×M16—22no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C4×Dic22—41no—
41C4×Dic22—41no—
42C11×C4⋊C8—41no—
43C11×C4⋊C8—41no—
44C11×#101—42no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11905—111nomaximal, Sylow
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11SD1612yes—
61C2×Q8×C11Q1612yes—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C11×M16—42no—
76C11×M16—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—42no—
94C2×C11⋊C8—42no—
95#2581—111no—
96#1801D1111yescharacteristic
97#1461—111no—
98#1354—112no—
99#1353—112no—
100C23×C11C2×C22⋊C411yescharacteristic
101Q8×C11—42no—
102Q8×C11—42no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11#9911yescharacteristic
118C2×C4×C11#10312yes—
119C2×C4×C11#10312yes—
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11C2×Q1611yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—42no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133Dic22—42no—
134Dic22—42no—
135C8×C11—82no—
136C11⋊C8—82no—
137C2×C4×Q8—111no—
138C2×C4×Q8C2×D1111yescharacteristic
139#431—221no—
140#423—21no—
141C2×#101—21no—
142#400—111no—
143#400—111no—
144#395—111no—
145#395—111no—
146#391—221no—
147#389—221no—
148#387—221no—
149#387—221no—
150#382—111no—
151#343C2×D1112yes—
152#324—112no—
153#324—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#9911yescharacteristic
157C22×C11C2×#10311yescharacteristic
158C22×C11#42111yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168Dic11—42no—
169Dic11—81no—
170Dic11—81no—
171Dic11—81no—
172C22×Q8—111no—
173C22×Q8C22⋊D1111yescharacteristic
174C2×M16—22no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—441no—
178C4×Q8—441no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4C4×D1111yescharacteristic
185C2×C4⋊C4D4411yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C42—221no—
188C2×C42C4×D1111yescharacteristic
189C2×C42D4411yescharacteristic
190C2×C42C22⋊D1111yescharacteristic
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—441no—
194#101—42no—
195C22⋊C8—222no—
196C4×C8—441no—
197#95—111no—
198#95—111no—
199#95—221no—
200#95—221no—
201#95—221no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11#152011yescharacteristic
209C2×C11#212011yescharacteristic
210C2×C11#213311yescharacteristic
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—441no—
214C2×Q8—442no—
215C2×Q8#432412yes—
216C2×Q8#432612yes—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—42no—
229M16—42no—
230C2×C8—42no—
231C2×C8—442no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—441no—
236C4⋊C4—442no—
237C4⋊C4—442no—
238C4⋊C4—442no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—442no—
248C11#1190511yescharacteristic, complemented, Sylow
249C23C2×(C2×D11)⋊C411yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—442no—
253Q8—442no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—222no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—441no—
274C2×C4—442no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4#6687011yescharacteristic
279C2×C4#6687011yescharacteristic
280C2×C4#6687412yes—
281C2×C4#6687412yes—
282C2×C4C2×#432411yescharacteristic
283C2×C4C2×#432611yescharacteristic
284C8—82no—
285C8—882no—
286C22—21no—
287C22—21no—
288C22C2×#6687011yescharacteristic
289C22C2×#6687411yescharacteristic
290C22#1062261811yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—442no—
301C4—881no—
302C4—881no—
303C4—881no—
304C2—21no—
305C2—21no—
306C2#1306718711yescharacteristic
307C2#1307025811yescharacteristic
308C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1801D11
hypocenterC11#11905
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
248. C11#11905semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130739782
#130669402
#130666452
#130666422
C11×#18012
#1190511